“When we talk mathematics, we may be discussing a secondary language, built on the primary language truly used by the central nervous system. Thus the outward forms of our mathematics are not absolutely relevant from the point of view of… — John von Neumann Copy Share Image
Truth is much too complicated to allow anything but approximations. — John von Neumann Copy Share Image
Problems are often stated in vague terms... because it is quite uncertain what the problems really are. — John von Neumann Copy Share Image
It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful… — John von Neumann Copy Share Image
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore. — John von Neumann Copy Share Image
There is no point in being precise if you do not even know what you are talking about. — John von Neumann Copy Share Image
The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations… — John von Neumann Copy Share Image
If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that. — John von Neumann Copy Share Image
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than… — John von Neumann Copy Share Image
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a… — John von Neumann Copy Share
Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will… — John von Neumann Copy Share Image
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other. — John Von Neumann Copy Share Image
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. — John von Neumann Copy Share Image
